Water polo is great

by zephyrcrush78, Sep 12, 2016, 4:17 AM

Possibly my first USAMO P6? :maybe:
Also Tidbit is actually something this time unlike my previous post where I just did it to copy SSD
USAMO 2006/6 wrote:
Let $ABCD$ be a quadrilateral, and let $E$ and $F$ be points on sides $AD$ and $BC$, respectively, such that $AE/ED=BF/FC$. Ray $FE$ meets rays $BA$ and $CD$ at $S$ and $T$ respectively. Prove that the circumcircles of triangles $SAE$, $SBF$, $TCF$, and $TDE$ pass through a common point.

Solution

Tidbit

Comment

6 Comments

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
what is water polo :maybe:

by skipiano, Sep 12, 2016, 4:22 AM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Water polo is the best sport ever.

by zephyrcrush78, Sep 12, 2016, 4:32 AM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
What... you get something very inappropriate if you search it on google

by skipiano, Sep 12, 2016, 4:42 AM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
uh... i get this: https://en.wikipedia.org/wiki/Water_polo as the first result...

by budu, Sep 12, 2016, 5:30 AM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
ZEP YOU'RE SCARING ME HOW ARE YOU SO OP

by shiningsunnyday, Sep 13, 2016, 4:24 PM

The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
I'm only mildly proficient at geo... anything else scares me to death D:

by zephyrcrush78, Sep 13, 2016, 7:26 PM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

avatar

shiningsunnyday
Archives
- May 2017
Shouts
Submit
  • this guy is an absolute legend. much love wherever you are Michael

    by LeonidasTheConquerer, Aug 5, 2024, 9:37 PM

  • amazing blog

    by anurag27826, Jun 17, 2023, 7:20 AM

  • hi i randomly found this

    by purplepenguin2, Mar 1, 2023, 8:43 AM

  • can i be a contributor please?

    by cinnamon_e, Mar 10, 2022, 6:58 PM

  • orzorzorzorzorzorozo

    by samrocksnature, Jul 16, 2021, 8:25 PM

  • 2021 post

    by the_mathmagician, May 5, 2021, 3:28 PM

  • Let $ ABC$ be an equilateral triangle of side length $ 1$. Let $ D$ be the point such that $ C$ is the midpoint of $ BD$, and let $ I$ be the incenter of triangle $ ACD$. Let $ E$ be the point on line $ AB$ such that $ DE$ and $ BI$ are perpendicular. $ \

    by ARay10, Aug 25, 2020, 5:55 PM

  • Nice blog! :)

    by User526797, Jan 12, 2020, 4:48 PM

  • oh my gosh it's been so longggggg.... contrib? what does that mean?

    by adiarasel, Dec 1, 2019, 8:31 PM

  • 2019 post

    by piphi, Aug 10, 2019, 6:32 AM

  • hi contrib please

    by Emathmaster, Dec 27, 2018, 5:38 PM

  • hihihihihi contrib plzzzzz

    by haha0201, Aug 20, 2018, 3:58 PM

  • contrib please

    by Max0815, Aug 1, 2018, 12:35 AM

  • contrib /charmander

    by mathmaster2000, Apr 16, 2017, 4:59 PM

  • for contrib

    by SomethingNeutral, Mar 30, 2017, 7:57 PM

270 shouts
Tags
About Owner
  • Posts: 1350
  • Joined: Dec 19, 2014
Blog Stats
  • Blog created: Jun 11, 2016
  • Total entries: 193
  • Total visits: 30959
  • Total comments: 579
Search Blog
a